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A two-stage contact process on scale-free networks. (English) Zbl 1301.92076

Summary: We study a two-stage contact process on scale-free networks as a model for the spread of epidemics. We show that any virus starting from a single vertex with arbitrarily small infection rates can last for a super-polynomial time with positive probability if the power law exponent \(\alpha>2\). This is in sharp contrast with the mean-field analysis. The estimation of the metastable density is also provided.

MSC:

92D30 Epidemiology
05C80 Random graphs (graph-theoretic aspects)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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